3m^2-12m-38=-5

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Solution for 3m^2-12m-38=-5 equation: 


Simplifying
3m2 + -12m + -38 = -5

Reorder the terms:
-38 + -12m + 3m2 = -5

Solving
-38 + -12m + 3m2 = -5

Solving for variable 'm'.

Reorder the terms:
-38 + 5 + -12m + 3m2 = -5 + 5

Combine like terms: -38 + 5 = -33
-33 + -12m + 3m2 = -5 + 5

Combine like terms: -5 + 5 = 0
-33 + -12m + 3m2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + -4m + m2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + -4m + m2)' equal to zero and attempt to solve:

Simplifying
-11 + -4m + m2 = 0

Solving
-11 + -4m + m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -4m + 11 + m2 = 0 + 11

Reorder the terms:
-11 + 11 + -4m + m2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -4m + m2 = 0 + 11
-4m + m2 = 0 + 11

Combine like terms: 0 + 11 = 11
-4m + m2 = 11

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 11 + 4

Reorder the terms:
4 + -4m + m2 = 11 + 4

Combine like terms: 11 + 4 = 15
4 + -4m + m2 = 15

Factor a perfect square on the left side:
(m + -2)(m + -2) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(m + -2) equal to 3.872983346 and -3.872983346.


Subproblem 1
m + -2 = 3.872983346

Simplifying
m + -2 = 3.872983346

Reorder the terms:
-2 + m = 3.872983346

Solving
-2 + m = 3.872983346

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + m = 3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + m = 3.872983346 + 2
m = 3.872983346 + 2

Combine like terms: 3.872983346 + 2 = 5.872983346
m = 5.872983346

Simplifying
m = 5.872983346


Subproblem 2
m + -2 = -3.872983346

Simplifying
m + -2 = -3.872983346

Reorder the terms:
-2 + m = -3.872983346

Solving
-2 + m = -3.872983346

Solving for variable 'm'.

Move all terms containing m to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + m = -3.872983346 + 2

Combine like terms: -2 + 2 = 0
0 + m = -3.872983346 + 2
m = -3.872983346 + 2

Combine like terms: -3.872983346 + 2 = -1.872983346
m = -1.872983346

Simplifying
m = -1.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {5.872983346, -1.872983346}
Solution
m = {5.872983346, -1.872983346}

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